Since M. O. Kramer reported successful experimental results in 1957, there have been repeated attempts to reduce frictional drag in turbulent fluid flow over a surface by applying a passive compliant coating. Experimental results in this area have been mixed. Most investigators have reported a drag increase, while only a few have claimed drag reduction for turbulent flow. A number of theoretical studies have characterized the stability of the laminar boundary layer over a deforming surface and other studies have characterized the reaction of a coating to a fluctuating load. However, no rigorous analytical technique has been previously reported that has been used to successfully design a drag-reducing coating for turbulent flow.
In the past, passive coatings were tested without specification and full characterization of critical physical parameters, such as the frequency dependent complex shear modulus, density, and thickness. In order to achieve and ensure drag reduction with a viscoelastic coating, a methodology is required for selecting appropriate material properties and for estimating anticipated drag reduction as a function of configuration and velocity.
Relevant background information for associated technical topics is available in the literature, and may be useful due to the technical complexity of this invention. A classical discussion of boundary layer theory, including formulation of Navier-Stokes and turbulent boundary layer equations, is provided in Boundary-Layer Theory, by Dr. Hermann Schlichting, published by McGraw Hill, New York, seventh edition, 1979. A discussion of structures and scales in turbulent flows can be found in Turbulence, 1975, McGraw Hill, written by J. O. Hinze, and in “Coherent Motions in the Turbulent Boundary Layer,” in Annual Review of Fluid Mechanics, 1991, volume 23, pp. 601-39, written by Steven K. Robinson. Background on Reynolds stress types of turbulence models is found in the chapter, “Turbulent Flows: Model Equations and Solution Methodology,” written by Tom Gatski, and included in the Handbook of Computational Fluid Mechanics, published by Academic Press in 1996. Equations in fluid and solid mechanics are often expressed in indicial, or tensor, notation, for compactness. Chapter 2 in the text A First Course in Continuum Mechanics, by Y. C. Fung, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1977, provides a brief introduction into tensor notation for mechanics equations. An introduction to finite difference methods, which are used to solve the system of momentum and continuity equations for a turbulent fluid, is provided in the text, Computational Fluid Dynamics for Engineers, written by Klaus Hoffman, and published in 1989 by the Engineering Education System i Austin  in Austin, Texas. Descriptions of measured and mathematically modeled physical properties of polymers are found in the text, Viscoelastic Properties of Polymers by J. D. Ferry, Wiley, New York, 1980, 3rd edition. The article, “Loss Factor Height and Width Limits for Polymer Relaxation,” by Bruce Hartmann, Gilbert Lee, and John Lee, in the Journal of the Acoustical Society of America Vol. 95, No. 1, January 1994, discusses mathematical characterization of shear moduli for real viscoelastic, polymeric materials, including those approximated by the Havriliak-Negami approach.
Recently in the international literature (K. S. Choi, X. Yang, B. R. Clayton, E. J. Glover, M. Atlar, B. N. Semonev, and V. M. Kulik, “Turbulent Drag Reduction Using Compliant Surfaces,” Proceedings of the Royal Society of London, A (1997) 453, pp. 2229-2240). Choi et al. reported experimental measurements of up to 7% turbulent friction drag reduction for an axisymmetric body coated with a viscoelastic material. These experiments were performed in the United Kingdom, using coatings designed and fabricated in Russia at the Institute of Thermophysics, Russian Academy of Sciences, Novosibirsk, by a team headed by B .N. Semenov. The basic design approach was outlined in “On Conditions of Modelling and Choice of Viscoelastic Coatings for Drag Reduction,” in Recent Developments in Turbulence Management, K. S. Choi, ed., 1991, pp. 241-262, Dordrecht, Kluwer Publishers. The Novosibirsk design approach is semi-empirical in nature, and does not take into account the full characterization of the complex shear modulus of the viscoelastic material, namely, the relaxation time of the material. The Novosibirsk design approach does take into account frequency-dependent material properties. Furthermore, the Novosibirsk concept is valid only for a membrane-type coating, such as a film which coats a foam-rubber saturated with water or glycerine, and where only normal fluctuations of the surface are considered.
The structure of coatings intended for drag reduction has been addressed in the international literature, starting with the 1938 patent No. 669-897, “An Apparatus for the Reduction of Friction Drag,” issued in Germany to Max O. Kramer. Kramer later received a patent in 1964, U.S. Pat. No. 3,161,385, and in 1971, U.S. Pat. No. 3,585,953 for coatings to extend laminar flow in a boundary layer. Soviet inventor's certificates, such as “A Damping Covering,” USSR patent 1413286, Publication 20.01.1974, Bulletin of the Inventions 14, by V. V. Babenko, L. F. Kozlov, and S. V. Pershin, “An Adjustable Damping Covering,” USSR patent 1597866, Publication 15.03.1978, Bulletin of the Inventions 110, by V. V. Babenko, L. F. Kozlov, and V. I. Korobov, and “A Damping Covering for Solid Bodies,” USSR patent 1802672, Publication 07.02.1981, Bulletin of the Inventions 15, by V. V. Babenko and N. F. Yurchenko, have also described the structure of drag-reducing coatings comprised of viscoelastic materials. These inventor's certificates identified the three-dimensional structure within a drag-reducing coating, but do not address the methodology for choosing appropriate parameters of the viscoelastic materials to be used in the manufacture of such coatings. Structural features include multiple layers of materials, longitudinal, rib-like inclusions of elastic, viscoelastic, or fluid materials, and heated elements. Viscoelastic coatings may be combined with other forms of structure, such as longitudinal riblets molded on or within the surface of the coating. As described in the international literature in publications such as “Secondary Flow Induced by Riblets,” written by D. B. Goldstein and T. C. Tuan, and published in the Journal of Fluid Mechanics, volume 363, May 25, 1998, pp. 115-152, two-dimensional, rigid riblets alone have been shown experimentally to reduce surface friction drag up to about 10%.